- Wed Dec 18, 2024 12:37 pm
#111124
Hi Landphil!
Let's take a look at the two perspectives being debated here, which are introduced in lines 18 through 24:
"The debate centers around whether language corresponds in some essential way to objects and behaviors, making knowledge a solid and reliable commodity; or, on the other hand, whether the relationship between language and things is purely a matter of agreed-upon conventions, making knowledge tenuous, relative, and inexact."
So, we have a perspective that a) language corresponds in an essential and concrete way to objects and behaviors, and b) language is based entirely upon agreed-upon conventions.
Now, let's take a look at Paragraph Three. Paragraph three discusses the latter theory (the theory that language is based entirely upon agreed-upon conventions), and explains it at length. Then, it proceeds to apply this theory to mathematical language.
Answer Choice B states that the primary purpose of Paragraph Three is to: "elaborate the position of linguists who believe that truth is merely a matter of convention."
If we look at the text of Paragraph Three, specifically lines 29 through 32, we can see this exact discussion at play: "These linguists argue that, in the pursuit of knowledge, a statement is true only when there are no promising alternatives that might lead one to question it." The conventionalist theory argues that there is no objective truth when it comes to language, since there can be no concrete and exact correspondence between language and concepts, objects or behaviors. Since the agreed-upon conventions that language is based on are subjective and malleable, there can be no objective truth. This applies in mathematics, where mathematical statements/language are only taken as true so long as there is no compelling indication to question it. Therefore, truth is just a convention, thus making Answer Choice B our correct answer.
Let's take a real world example-- for centuries, it was widely accepted to be true that the smallest object in the universe was a molecule. Then, the atom, a smaller object, was discovered and proven around the 1800s. At this point, the accepted truth of the smallest object in the universe changed. No objective truth changed, only our understanding of conventions.
I hope this helps!